The Radiative Corrections to the Mass of the Kink Using an Alternative Renormalization Program

TL;DR

This paper calculates the quantum correction to the mass of a kink in 1+1 dimensional $^4$ theory using a new renormalization approach that accounts for translational symmetry breaking and topological features.

Contribution

It introduces an alternative renormalization program that naturally incorporates the kink's topological and translational properties, leading to uniquely defined position-dependent counterterms.

Findings

Computed the kink mass correction up to next-to-leading order.

Highlighted differences between the new method and previous results.

Demonstrated the effectiveness of the alternative renormalization approach.

Abstract

In this paper we compute the radiative correction to the mass of the kink in $\phi^4$ theory in 1+1 dimensions, using an alternative renormalization program. In this newly proposed renormalization program the breaking of the translational invariance and the topological nature of the problem, due to the presence of the kink, is automatically taken into account. This will naturally lead to uniquely defined position dependent counterterms. We use the mode number cutoff in conjunction with the above program to compute the mass of the kink up to and including the next to the leading order quantum correction. We discuss the differences between the results of this procedure and the previously reported ones.